Final answer:
An isosceles triangle with angles measuring 50°, 50°, and 80° will keep the same angle measurements after translation, rotation, and reflection because these transformations do not alter the shape or size of the triangle.
Step-by-step explanation:
When we consider an isosceles triangle with angles measuring 50°, 50°, and 80°, we must remember that all triangles have three sides and the sum of their angles adds up to 180 degrees. Thus, when we apply different geometric transformations to the triangle, the angles remain unchanged if the transformation does not alter the shape or size of the triangle.
A translation is a slide that moves every point of a figure the same distance in the same direction. Under translation, the shape, size, and angles of the triangle remain the same. So, the answer is Yes, the angles will still measure 50°, 50°, and 80° after translation.
A rotation involves turning a figure around a fixed point called the center of rotation. The angles of the figure are preserved, so the triangle's angles still measure 50°, 50°, and 80° after rotation. Therefore, the answer is Yes.
A reflection is a flip over a line where each point of the original figure and its image are the same distance from the line of reflection. Reflection does not change the size or angles of the figure, so the triangle will have the same angle measurements after a reflection. Consequently, the answer is Yes.